It originally referred to those from Denham, Buckinghamshire, Denham, Suffolk and Denholme, Yorkshire. The name of Denham may have come from Brittany as "de Dinan" and carried to Scotland by Alan, Baron de Dinan.. See The name "Denham" by Virginia Denham.
Text adapted from Wikipedia, CC BY-SA 4.0. Photograph: Rosser1954 (see Commons), Wikimedia Commons.